{"paper":{"title":"Liouville-type results for the CR Yamabe equation in the Heisenberg group","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"J\\'er\\^ome V\\'etois, Joshua Flynn","submitted_at":"2023-10-21T16:07:30Z","abstract_excerpt":"We obtain Liouville-type results for solutions to the CR Yamabe equation in $\\mathbb{H}^n$, which extend a result obtained by Jerison and Lee for solutions in $L^{2+2/n}(\\mathbb{H}^n)$. We obtain our results under either pointwise conditions or integral conditions at infinity. In particular, our results hold for all bounded solutions when $n=2$ and solutions satisfying a pointwise decay assumption when $n\\ge3$. The proofs rely on integral estimates combined with a suitable divergence formula."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.14048","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2310.14048/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}